Newtonian mechanics and Punching

Wai Jia: The Kung Fu Forum Wing Chun
1

Just some thoughts …..

list=1 F = m x a
(Force = mass x acceleration)[/list=1]
Force required to move mass m (your fist) with acceleration a. This is just a really simplified model.

Since a = rate of change of velocity with respect to time, we can also write:

list=1 F = m x dv/dt
Where dv/dt is the rate of change in velocity.[/list=1]
So if you imagine accelerating your fist, from rest, then to achieve the greatest force you want to either get to the highest speed possible or do it in the smallest time interval; preferably both.

But what happens when you make contact? Well the idea is to try and transfer all the momentum (or energy, used interchangeably although they are different things) of your punch into your opponent.

Ideally you’d transfer 100%, which brings your fist to a rest and all the momentum/energy is transferred into your opponent. Imagine the executive “cat’s cradle” toy, where you’ve got a row of steel balls suspended by string from a frame. You draw one ball back, it hits the other balls and the ball on the other end is flicked back. Well that what you want your punch to do.

We can re-formulate equation (2), because momentum p = m x v (mass x velocity). So:

list=1 F = dp/dt[/list=1]
The greater the change in momentum the greater the force imparted to the opponent. So if the opponent is at rest, or coming towards you, then the momentum of your punch will have a greater effect than if he was moving away.

If we look at things from an energy viewpoint. The kinetic energy of your punch, converted from your muscular potential energy, is given by:

list=1 1/2 x m x v2
(half x mass x velocity squared).[/list=1]
The faster your fist is moving, the more kinetic energy you will impart to your opponent at contact.

“But what about heavy weight boxers?”, I hear you ask; “they can punch harder than light weights”. Probably many reasons for this, but I can think of 2 off the top of my head:

[list=1]1) I’m only describing the fist, propelled by the bicep/tricep muscle pair. In reality you’re punching with your whole body and therefore the larger the body mass, the more momentum you can deliver.

  1. There may be a limit to how quickly one can move a fist, and it may have nothing to do with how big you or your muscles are.[/list=1]
    So for a given mass, I think it may be better for someone to work on their punching speed rather than just get bigger. As has been said before on this forum, there are many kinds of speed in WC (or any martial arts for that matter).
2

Probably it’s easier to increase body mass, or even just arm mass, in relation to the square of the velocity. Is it easier to gain 9 kg, or to increase the velocity of your punch by 3 m/s (which is a LOT)?

3

Originally posted by Tak
Probably it’s easier to increase body mass, or even just arm mass, in relation to the square of the velocity. Is it easier to gain 9 kg, or to increase the velocity of your punch by 3 m/s (which is a LOT)?
Yep, good point there. Is it easy to gain 9 kg of arm mass? That’s 19 (British) pounds, which seems like a bloody big increase in bicep size!!

However, if we’re talking dv/dt. Then decreasing the time it takes to reach your previous speed from rest (i.e. improving your acceleration) generates more force.

dv = velocity/speed at impact - rest speed (0), so dv is positive and is effectively the speed at impact.

4

I think an important point when discussing equations like this is to always step back and ask yourself how can you benefit from such a mental exercise. How is it helping you to train better and improve in your wing chun? In the end you need to learn to relax more for speed and power? train your root better? work harder more in general, or in specifics? Do you need equations to tell you this?

5

Sure, just using a simple example. Also, if we’re figuring body mass instead of just arm mass, 19 pounds is almost nothing. It would be very difficult to increase your final velocity by 3 m/s, too. It seems like there is a diminishing returns barrier attached to speed that isn’t quite as stringent for mass.

6

Tak- Schroedinger’s cat could possibly have something more nsightful to contribute to the dicussion of a wing chun punch- more that Newtonian mechanics possibly?

7

Hmm, are you suggesting that the punch exists in a dual state of hit and miss until both parties check to see if it has landed?

Or that WC practitioners should be confined in a small box?

8

I think an important point when discussing equations like this is to always step back and ask yourself how can you benefit from such a mental exercise. How is it helping you to train better and improve in your wing chun? In the end you need to learn to relax more for speed and power? train your root better? work harder more in general, or in specifics? Do you need equations to tell you this?

Hmmm. Does bashing shaolin-do benefit your training? Or does surfing the net benefit your training? Or does drinking beer benefit your training? Maybe it is just a discussion. Nothing more. Maybe some of us like to talk about physics :eek: Yes i know that sound crazy, but guess i am, since i’m also studying it (some) :smiley:

Gotta get back to this tomorrow.

9

Does bashing shaolin-do benefit your training?
No, it reinforces any negative attitudes I have.

Or does surfing the net benefit your training?
Yes, it gives me food for thought. Except this forum.

Or does drinking beer benefit your training?
Yes! Carbo loading!

10

Analysing the physics behind the expression of power in a good wing chun punch gets quite tricky quite quickly - its about kinetic chains. It also depends which punch you’re talking about - with a step, with a shift, etc… Go back and read the old neija lists with Mike Sigman if you want to see some entertaining arguments about physics and jing!

If you do want to put your physics to good use, i’d suggest looking into the mechanics of wing chun footwork as a place to start.

11

Crimsonking is correct imo.

12

Yeah I only put this thread up after a previous thread on the power of Wing Chun punches got a bit long and somewhat off topic.

I only chose to describe a very simplified situation where only the fist is moving, which I acknowledge is not very realistic.

A stepping punch I think would be quite easy to describe. The momentum of the body is added to momentum of the punch:

Total momentum = M x V + m x v
(M = body mass, V = body speed, m = fist mass, v = fist velocity)

So this adds credence to the belief that a heavy fighter will punch harder.

As for a turning punch, i.e. twisting the torso about the centre line, I don’t have the equations at hand for angular momentum and it’s conversion into linear momentum. I’ll return to this in a later post.

By the way can any one give me an estimate to how quickly they “twist”. Answers on a postcard and in units of radians per second!! :wink:

13

Originally posted by CFT
So this adds credence to the belief that a heavy fighter will punch harder.

What if we tweak the question to the heavier fighter having ‘the potential’ to punch harder. Without that, it sounds like a question of individual development in the hitter. We all know small people who really pack some punch.

14

After reading all the posts in this thread, I can’t help but think about the story of the bumble bee. According to the mathematical calculations of aeronautics engineers and scientists, the bumble bee cannot fly. It’s wings are too small relative to its big body. But the bumble doesn’t know that. It is not concerned about all the mathematical calculations saying that it can’t fly. So, it goes ahead and fly!

IMHO, constant practice is a better way to improve our punching power than all the mathematical equations combined.

15

Originally posted by Wingman
[B]After reading all the posts in this thread, I can’t help but think about the story of the bumble bee. According to the mathematical calculations of aeronautics engineers and scientists, the bumble bee cannot fly. It’s wings are too small relative to its big body. But the bumble doesn’t know that. It is not concerned about all the mathematical calculations saying that it can’t fly. So, it goes ahead and fly!

IMHO, constant practice is a better way to improve our punching power than all the mathematical equations combined. [/B]
That’s a good story and underlines the problem of oversimplifying the problem. The “model” that proves the bumble bee cannot fly assumes that the bee flies in a fixed wing mode, like an aeroplane. Therefore given it’s wing size, it was calculated that it couldn’t possibly generate enough lift, and therefore couldn’t fly. Obviously nonsense!!

Subsequently, scientists have discovered that the bee’s wing actually moves in a more complex figure-of-eight pattern and I think that it can generate lift in both the down- and upward-stroke (if I remember correctly).

Obviously mathematics is no substitute for practice, but sometimes mathematical models provide us with insights that are counter-intuitive. Many modern athletes and sportsmen/women make use of the techniques of bio-mechanics and sports science in order to improve their performance. Obviously they have to train and practice as well.

16

What about the seeming trade-off between dize and speed? I’ve often noticed that people who gain a lot of muscle mass often lose speed. Also, if a fighter is twice as big as you, that does not mean that his arm (the object that has momentum during a punch) is twice as heavy as your arm… So the payoff for having increased mass under this admittedly limited model is arguable.

17

What about the seeming trade-off between dize and speed? I’ve often noticed that people who gain a lot of muscle mass often lose speed.

Anton, gaining muscle does not equal to losing speed. Thats just a myth. You can gain muscle and increase speed if you train correctly (i know i did).

Also, if a fighter is twice as big as you, that does not mean that his arm (the object that has momentum during a punch) is twice as heavy as your arm… So the payoff for having increased mass under this admittedly limited model is arguable.

The momentum does not come from the arm alone. Read a previous post describing a stepping punch. Also, twisting movement of the torse adds momentum (which is higher when the body has larger mass), although this wasn’t in the model.

18

In terms of adding a twist about your centre-line in order to add impetus to your punch:

(1) Angular momentum L = I x w
where I = moment of inertia
and w = angular velocity

This is similar to the formula for linear momentum:

(2) Linear momentum p = m x v
where m = mass
and v = linear velocity

The rotational kinetic energy, Er = 1/2 x I x w2 (w-squared)
Similar to linear kinetic energy, El = 1/2 x m x v2 (v-squared)

So the faster we can twist or the larger the moment of inertia the more momentum or energy we can deliver to the opponent. As my critics like to point out … bleedin’ obvious innit? Yep 'fraid so!

Heard of the Law of Conservation of Angular Momentum? If you’ve seen figure skater on TV, when they do the final spin in their routines. They start turning with their arms out, and as they draw their arms in they start to spin faster.

When they draw their arms in they are reducing their moment of inertia; since their angular momentum is conserved (bar friction) this means that their rotational velocity must increase.

I don’t really think this is what we do when we swivel and punch, but you can see that there is a mathematical description for the energies involved.

Moment of inertia, I, for the torso is something like: 1/2 x M x R2
where M is the body mass and R is the distance from the centre line to the shoulder. Assuming the WC practioner is a cylindrical mass or dummy!! :stuck_out_tongue:

Look here for some pictures of common shapes and their moments of inertia:
http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#cmi

As you can see this very simplistic model just assumes that we’re solid rods or blocks. Nothing like a real anatomical model to take into account musculature and tendons.

So my advice is to spin round and round really fast, creating a path of destruction wherever you go :wink:

19

About the Impossible

Along this line, there was a Canadian study done once by a group of scientists that tested the natives up North (used to be called Eskimos but now are called Inuits). Anyway after extensive aptitude and IQ testing the report was written up that concluded that these people did not have the intelligence nor aptitude to deal with the harse Winters in the North and survive. Well obviously they have been doing it for hundreds of years. So point was that these kinds of tests were often quite useless.

Often as in the Bee example the mathematical model is not representative of the thing being modeled. There was also a study done a long time ago that trains can never go faster than 30 miles an hour. Why? Well when a train goes so fast like that, all the oxygen will get sucked out of the train and then everyone will suffocate to death.

Originally posted by CFT
[B] That’s a good story and underlines the problem of oversimplifying the problem. The “model” that proves the bumble bee cannot fly assumes that the bee flies in a fixed wing mode, like an aeroplane. Therefore given it’s wing size, it was calculated that it couldn’t possibly generate enough lift, and therefore couldn’t fly. Obviously nonsense!!

Subsequently, scientists have discovered that the bee’s wing actually moves in a more complex figure-of-eight pattern and I think that it can generate lift in both the down- and upward-stroke (if I remember correctly).

Obviously mathematics is no substitute for practice, but sometimes mathematical models provide us with insights that are counter-intuitive. Many modern athletes and sportsmen/women make use of the techniques of bio-mechanics and sports science in order to improve their performance. Obviously they have to train and practice as well. [/B]

20

Hi Ray- good post on the issue of whther the model is appropriate for the study.
Regarding Inuit-
Alaskan Malamutes evolved out of the the AKC recognition-their roots (including mine) are in the Inuit world and the Inuit dog. In a book on studying the intelligence of dogs -malamutes were ranked lower than border collies or poodles. If one looks at the criteria used—
the dogs that performed the specified tasks-usually obedience oriented were ranked higher- the malamute world does not rank obedience as an important value… but creative survival in 70 below zer0 50 mph winds per Adm. Scott’s Antartic expeditions?.. a malamute is a creative survivor-
so also in the Arctic.

The Inuit and their dogs had the appropriate intelligence to a high degree in their environment.

If you change the function- you can geta different result- the border collie for herding sheep, the poodle for circus tricks and the
hybrid alaskan husky for competitive racing (Iditarod).
Then there are training and adaptation variables- but that’s a different story.

In science- before going to the equations- appropriate analysis of the nature of the problem- is a key step.